The present invention relates to a method of making a finite element model of a pneumatic tire used in a finite element method to analyze tire performance, tire behavior and the like and suitably used to simulate a system including pneumatic tires.
In recent years, as the computers"" performances have been remarkably improved, finite element methods are used in the field of pneumatic tires, and not only static analyses of a tire but also dynamic analyses of a tire and simulation are becoming possible. As a result, it becomes possible to estimate various tire performances accurately without making actual tires.
In the laid-open Japanese patent application JP-A-11-153520 (corresponding to U.S. Pat. No. 6,199,026), a finite element tire mode is disclosed, wherein, as shown in FIG. 12, a cord layer (b) is modeled by a quadrangular membrane element (d) and a rubber layer (c) is modeled by a hexahedral solid element (e). In case of the FIG. 12 example, the number of the elements is five and the number of nodes of the superposed elements is twenty four. Thus, the computation load is not so light.
On the other hand, it is strongly required to simulate and analyze a system including a vehicle body, tires and roads in order to reduce the research and development time and cost for the tires and improve overall tire performance including a vehicle body.
In case of the above-mentioned finite element tire model, the total element number and total node number of a set of tires are still large, and those of the system becomes very large. Therefore, the computation time becomes very long, and at the worst the computation becomes impossible due to the memory size limit.
It is therefore, an object of the present invention to provide a method of making a finite element model of a pneumatic tire, in which the number of finite elements can be decreased and speedup of computation time is possible without sacrificing accuracy of analyses and simulation.
According to the present invention, a method of making a finite element model of a pneumatic tire comprises
dividing a pneumatic tire into a plurality of modeling units each of which is to be modeled by one or more finite elements so that the modeling units include modeling units each of which is a layered complex of at least one cord layer and at least one rubber layer, and
modeling each of the modeling unit which is a layered complex, by a shell element provided with a plurality of integral points corresponding to the at least one cord layer and at least one rubber layer.
A shell element itself has no thickness when viewed from the coordinates of its nodes, but it may have data relating to the thickness of the objective layer(s) in addition to other data relating to the physical properties, e.g. Young""s modulus, Poisson""s ratio, specific gravity and the like.
Contrary, a membrane element is an element such that forces to be considered are only those in its plane, namely, it delivers only tension, compression and shearing force along the plane. Thus, it has no data relating to forces outside its plane and accordingly bending stress, bending stiffness and the like can not be handled. Therefore, it may be said that a major difference between a shell element and a membrane element is that the shell element has a bending stiffness but the membrane element dose not have its bending stiffness.